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I don't have any previous experience with time measurements, and clocks, but for some reason I did find the subject of clock noise fascinating enough to make me purchase a synchronome on ebay and attempt some measurements to satisfy my curiosity.
Let me describe what I did about the energetics of this clock, it helped me to develop some intuition about it and hopefully will encourage others to report their findings.
I have tested first the pendulum energy losses as a function of the swing amplitude for the pendulum alone, starting larger than usual oscillations and letting them decay while measuring the pendulum speed.
I have chosen to measure the oscillation speed at its max, when the pendulum is in the middle of its oscillation, with an optical sensor, a Sharp, GP1A57HRJ00F from Sparkfun https://www.sparkfun.com/products/9299 which has the property of outputing a digital signal compatible with Arduino.
The sensor has been carefully positioned in the middle of the oscillation by balancing the pulses symmetry between the right and left going swing.
The sensor circuitry is the one of the Sparkfun breakout board.
The light beam is interrupted by a pin of known diameter (D) coaxial with the pendulum rod, in my case 4mm mounted on a "rigid spring". This simple design has the advantage that if the pendulum swings out of center the flexible tip bends away without causing any mechanical damage.
The pendulum max speed vmax is very approximately equal to the ratio of the pin diameter to the measured interception time (ΔT) of the light beam , vmax=D/ΔT.
The kinematics of the harmonic oscillator, the same of the pendulum aside from the circular error, tells us that the maximum speed and the swing amplitude are related by the pendulum frequency F, vmax = ω xmax, ω= 2 π F, the frequency F in the case of the Synchronome is equal to 1/2, so xmax = vmax/π .
Measuring the pendulum speed yields also the measurement of the angle of the pendulum swing θ equal in degrees to 180/π xmax = 180/π vmax/2 π F = 9.12 vmax T where T is the pendulum period.
The Q = 2π E/ ΔE measurement is even easier, it's independent from the pin/flag size, in the large Q approx Q = π Nc Δti / (Δti -Δti+1), where Nc is the number of periods in a cycle and Δti is the average of the photo-interrupt pulse length for the ith cycle, for a free running pendulum. With a synchronome Q can be measured between pulses with quite an acceptable accuracy too.
The data acquisition is a rudimentary one, it consists of an Arduino Uno running a super simple program:
where the key instruction pulseIn(pin,LOW,1500000) returns the length of the negative going sensor pulse in microseconds with a 1.5 10^6 μs of time out.
The noInterrupts() instruction is not essential but improves the accuracy and repeatability of the measurement by a factor of 10 in the author's experience. The calibration of my 3 arduinos when measuring 20 ms pulses was within 30 ppm.
The delay(10000) instruction line is there only to reduce the number of measurements displayed on the PC terminal with the PC time stamp (an arduino terminal option) which witnesses the actual delay between measurements. More measurements would produce a better statistics but measurent parsing allows for a quick spreadsheet analysis .
Arduino's clock accuracy, from which the accuracy of these measurements depends, doesn't look relevant to me for the present purpose but for the curious ones I have found a reference http://jorisvr.nl/article/arduino-frequency
A typical output is as follows
the time stamp of the measurement is followed on the same line by the measure in microseconds of the pendulum tip interrupting the photosensor light beam.
The time span of this measurement for a good range of angles can be hours, typical Qs being in the thousands and the period is 2s.
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